a What zscore separates the highest 25 from the rest of the

a. What z-score separates the highest 25% from the rest of the scores? b. What z-score separates the highest 60% from the rest of the scores? c. What z-score separates the lowest 30% from the rest of the scores? d. What z-score separates the lowest 80% from the rest of the scores?

Solution

a)
P ( Z < x ) = 0.75
Value of z to the cumulative probability of 0.75 from normal table is 0.674
P( x-u/s.d < x - 0/1 ) = 0.75
That is, ( x - 0/1 ) = 0.67
--> x = 0.67 * 1 + 0 = 0.674                  

b)
P ( Z < x ) = 0.4
Value of z to the cumulative probability of 0.4 from normal table is -0.253
P( x-u/s.d < x - 0/1 ) = 0.4
That is, ( x - 0/1 ) = -0.25
--> x = -0.25 * 1 + 0 = -0.253                  

c)
P ( Z > x ) = 0.7
Value of z to the cumulative probability of 0.7 from normal table is -0.52
P( x-u/ (s.d) > x - 0/1) = 0.7
That is, ( x - 0/1) = -0.52
--> x = -0.52 * 1+0 = -0.524                  

d)
P ( Z > x ) = 0.2
Value of z to the cumulative probability of 0.2 from normal table is 0.84
P( x-u/ (s.d) > x - 0/1) = 0.2
That is, ( x - 0/1) = 0.84
--> x = 0.84 * 1+0 = 0.842